Problem: Luis is 5 times as old as William. Six years ago, Luis was 7 times as old as William. How old is Luis now?
Explanation: We can use the given information to write down two equations that describe the ages of Luis and William. Let Luis's current age be $l$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $l = 5w$ Six years ago, Luis was $l - 6$ years old, and William was $w - 6$ years old. The information in the second sentence can be expressed in the following equation: $l - 6 = 7(w - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $l$ , it might be easiest to solve our first equation for $w$ and substitute it into our second equation. Solving our first equation for $w$ , we get: $w = l / 5$ . Substituting this into our second equation, we get: $l - 6 = 7($ $(l / 5)$ $- 6)$ which combines the information about $l$ from both of our original equations. Simplifying the right side of this equation, we get: $l - 6 = \dfrac{7}{5} l - 42$ Solving for $l$ , we get: $\dfrac{2}{5} l = 36$ $l = \dfrac{5}{2} \cdot 36 = 90$.